I made a list of size 6236, with randomly distributed numbers, and 294 out of 6236 numbers, have been purposefully adjusted, that they all have prime factors of nineteen and that their sum is 19 x 55049 .
And I have also made it such that their order placement in the 6236'th list size, where the 19 primefactor occurs, all sum to 17 x 55049 prime factor. Thus the prime factor occurring twice, 55049.
Please see the full list: https://pastebin.com/hApkBNcc Please click this: https://pastebin.com/9epAagc2
Thus I only sum, all the positions where the numbers have prime factor of 19, index placement. They total 17 x 55049 in prime factor sum.
And to make it more fun I purposefully, adjusted the instances where the 19 factor occurred, with adjusted factor, so instead where in the 4906'th position, the prime factor was 19 x 59(randomly produced initially) , I made it 19 x 49. The reason is that I wanted all the instances where the 19 prime factor occurs, sum all the values, and they give the same prime factor of 19 x 55049 (list B) as the total order sum of all the instances where 19 factor occurred, 17x 55049 (list A)
My entire purpose is to produce a Montecarlo simulation, where I purposefully, simulate the distribution of numbers from the list, https://pastebin.com/hApkBNcc, and emulating it with a randomly produced numbers from, a distribution that fits that list.
See picture: https://i.stack.imgur.com/9rVCp.jpg
In that do we expect to see, a prime digit of size 5 to be the same, and its produced by the distribution, often enough to reject the alternative hypothesis, that outside force have initially adjusted the list of numbers, such the same prime factor of size 5 occurrs. or that it is produced by the fitted distribution, randomly, and it is common.
So can the simulation detect that an outside force must have adjusted the list, such that a long primefactor was yielded the first time?
Monte Carlo simulation: After 500,000 experiments, all the instances where same prime factor occurs, of summing two list of values independent of each other, have
mean length of, or digit size: 1.5 (17,19,37,57,3,7,5) etc, (cases of 4 digits, and couple of 5 digits) standard deviation
0.49
Testing the null hypothesis: The long factor of 55049, of 5 digits are produced randomly, by a distribution, and no outside, human force have adjusted the list, for such an instance to occur.
5 - 1.5 / standard deviations = (5-1.5)/0.49 = 7 sigmas
Indeed after 500,000 experiments, only 4 cases occurred where 5 digit long factor, was produced where both list is the same primefactor.
Thus we can reject the null hypothesis that the long factor can be randomly produced by chance. And that a human must have adjusted the list to conform to list having the same 5 digit prime factor.
Is my assessment correct?